The NNLO gluon beam function for jet-veto resummation

We compute the gluon beam function for jet-veto resummation to next-to-next-to-leading order (NNLO) in the strong-coupling expansion. Our calculation is based on an automated framework that was previously used for the computation of the respective quark beam function, and which we significantly extended for the present calculation. In particular, the perturbative matching kernels are directly calculated in momentum space, without the need to perform an additional Mellin transform. We present results for both gluon and quark-initiated processes, which we cross-checked with an independent semi-analytical method that exploits the similarity of the beam functions to the more familiar case of transverse-momentum resummation. Our computation is relevant for jet-veto resummations at NNLL$'$ accuracy.